3 is a 0 of multiplicity 2

In a graph, when you touch or cross the x-axis, you can call that point “a zero.”  If whatever you’re drawing crosses the x-axis at “3,” then “3 is a 0.”  And “multiplicity” determines the shape of the thing you’re drawing at that point on the graph: the even numbers are parabolas, odds are dog-legs, and a “one” is a plain old line. “Multiplicity 2” means that at the point your thingy touches the x-axis, it does so in the shape of a parabola.  And although my class hasn’t gotten to this yet, I also know that it’s possible to have imaginary zeros.  I don’t know what you do with imaginary zeros.

Multiplicity has been a favorite word of mine since I was introduced to Bergson and Deleuze.  But I usually use the word in a sloppy way, as in: “we should have a multiplicity of voices represented in the literary canon.”  That’s a terrible thesis.  Bergson (who was a math whiz before he became a philosopher) wrote about both quantitative and qualitative multiplicities in much more precise, interesting ways.

Qualitative multiplicity is found in a singular experience that can’t be juxtaposed against another one.  One of Bergson’s examples is to imagine the stretch and elasticity of an elastic band. “Bergson tells us first to contract the band to a mathematical point, which represents ‘the now’ of our experience. Then, draw it out to make a line growing progressively longer. He warns us not to focus on the line but on the action which traces it”(from the Stanford Encyclopedia of Philosophy).  The duration of the stretch, the inherent tension, the smooth transition from point to line, the experience of it all: these elements contribute to the qualitative value of the multiplicity more than a static image (such as a graph of a trajectory like the one above) can preserve.

So there’s math + philosophy. And also + art: in Findings on Elasticity, editors Hester Aardse and Astrid Alben write, “Elasticity has no inhibitions.  Science has no inhibitions…As science continues to shamelessly stretch knowledge as far as it will go, unburdened by inhibitions, so art, in its limitless ways of expressing human experience, often confronts our inhibitions and suggests where we should put them.”  It’s a wonderful book full of experiments and installations and inventions exploring (it seems to me) the question: How do we authentically record, document, preserve, share, communicate our experience of the qualitative multiplicity of elasticity?

These notions of multiplicity-via-elasticity (math, philosophy, art) relate to the nomadic paths of protest librarians and the (often surprisingly divergent) paths of the libraries’ physical collections of books.  The question is, how do these trajectories represent both quantitative and qualitative multiplicities, and how can they be recorded in a meaningful way.  This is a project to root around in over the summer.

PS: This article about an exhibit called “Design and the Elastic Mind” randomly passed through my Facebook feed just as I posted this entry: Curator Forced to Kill Out-of-Control Bio-Art Exhibit

Things are linearly sloping up.

In the 1970s, I drew buttons and flashing lights on a cardboard box, cut slots on each end, and called it a computer.  You could write a question on a card, drop it into the entry slot, and it would come out the other end with the answer to your query.  The catch (a doozy): I had to write the answer on the card before you dropped it into the computer, since nothing actually happened on the inside of the box.

In math class, we’ve reached the chapter on functions. Functions do the kinds of things I very much wanted to make happen inside my cardboard computer. They are all about inputs and outputs: f(x) = [something crazy like 3x + 2].  f(x) — which is a fancy way to say y — is dependent on the input of x.  If you input something as “x” and only one thing is output at the other end, then it’s a function and you can happily plot x and f(x)  on a graph.

The linear model that we learned about last fall in statistics is closely related to all of this (or so it seems to me).  The linear model includes a slope (of a line), a y-intercept, and a relationship between dependent and independent variables.  They all work together to help predict the locations of dots on a regression analysis graph.  And I do love graphs.

This floated through my Facebook feed last week.  I can’t find a source for it.  But it makes about as much sense as linear models do when you don’t know algebra.

Understanding dependent and independent variables about killed me last semester, and they’re doing a number on me again.  But the cause/effect is clearer this time around.  My hat’s off to everyone who has to teach stats to someone like me, someone who doesn’t know what an algebraic function is.  I think this must have been the same kind of frustration as playing Mad Libs with someone who doesn’t know a noun from a verb from a postmodern platitude.

I feel triumphant in making this connection between functions and linear models (even if I still have some of it wrong).  And I am excited to think about how the spatial mapping of data (as dots) and relationships (as lines and slopes) is a much stronger undercurrent than I realized.  Maybe I should have known it.  But I didn’t.  But now I do.  So that’s progress, with the slope of my own linear progression again pointed upward and onward.